This is a phase I study to evaluate the safety, engraftment, and relative survival of single infusions of genetically engineered autologous CD34+ hematopoietic progenitor cells from HIV+ individuals without prior cytoreductive treatment. CD34+ cells will be enriched from peripheral blood obtained by apheresis from asymptomatic HIV+ individuals following mobilization with G-CSF. Isolated CD34+ cells will be divided into two cultures and grown on autologous stromal cultures for three days in growth medum containing the cytokines IL-3, IL-6 and SCF. During this time one culture will be transduced with a retroviral vector containing the anti-HIV double-ribozyme gene, which is directed toward the HIV tat and rev regions (L-TR/TAT-new, also referred to as TR/TAT-Rz and identified as TR/TAT(V) in the Drug Master File, appendix A.1 for reference authorization letters) and the second culture will be transduced with a control vector (LN; identified as LN (V) in the DMF) that does not encode for a ribozyme. The two cultures of engineered cells will then be mixed and infused into the subject. Following infusion, the ratios of cells containing each vector will be determined by vector-specific PCR from peripheral blood samples obtained at monthly intervals and from marrow samples obtained at 6,12, and 24 months. A relative increase in the frequency of cells containing the anti-HIV-1 TR/TAT ribozyme gene, compared to cells with the neutral marker gene, would imply that a selective survival advantage has been conferred to the cells by the anti-HIV-1 ribozymes. The goal of this project is to determine whether autologous PBPC that are transduced with a retrovirus containing a gene encoding ribozymes targeted to the tat and rev genes of HIV-1, can safely engraft after reinfusion I HIV-1 infected persons. Follow-up studies will determine: 1) The safety and feasibility of administering a double ribozyme-encoding retroviral vector in HIV+ subject by a single dose infusion of ex vivo transduced autologous CD34+ peripheral blood progenitor cells (PBPC). 2) Whether the tranduced cells are capable of engrafting and giving rise to transduced mature hematopoietic cels in the periphery without prior cyto-reduction treatment of the subject. 3) The comparative survivial of ribozyme-vector transduced HPC progeny cells versus control vector marked cells in the periphery.